Abstract: 

In this talk we will investigate a way to take two Dirichlet series attached to two different number fields and obtain some type of "convolution" generating function to find a way to relate the two field extensions to each other.  We will compute several examples, and focus on the case when the original Dirichlet series attached to the extensions are given by the Dedekind zeta functions. We will investigate the convergence, and possible analytic continuation in some cases. This talk will be intended for a general audience and will not assume any knowledge about automorphic representations or L-functions.